Question: Given $ m \angle CBD = 4x + 43$, $ m \angle ABC = 2x + 46$, and $ m \angle ABD = 149$, find $m\angle ABC$. $B$ $A$ $D$ $C$
Solution: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Substitute in the expressions that were given for each measure: $ {2x + 46} + {4x + 43} = {149}$ Combine like terms: $ 6x + 89 = 149$ Subtract $89$ from both sides: $ 6x = 60$ Divide both sides by $6$ to find $x$ $ x = 10$ Substitute $10$ for $x$ in the expression that was given for $m\angle ABC$ $ m\angle ABC = 2({10}) + 46$ Simplify: $ {m\angle ABC = 20 + 46}$ So ${m\angle ABC = 66}$.